Question

A)

Answer 1

Given:

The boundary line of an inequality is:

$2x+3y=6$

The solution set contains (0,0).

To find:

The inequality.

Solution:

The boundary line of an inequality is

$2x+3y=6$

Since (0,0) is in the solution set, therefore (0,0) satisfies the required inequality.

Taking LHS, we get

$LHS=2x+3y$

Substitute x=0 and y=0.

$LHS=2(0)+3(0)$

$LHS=0+0$

$LHS=0$

The right hand side of the given equation is 6.

$RHS=6$

We know that,

$0$

$LHS$

$2x+3y$

The boundary line is not a dotted line, it means the points on the boundary line are also included in the solution set. So, the inequality sign must be $\leq$.

$2x+3y\leq 6$

Therefore, the required inequality is $2x+3y\leq 6$.